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doc/build/html/commentary/stg.html
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<!DOCTYPE html>
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<html lang="en" data-content_root="../">
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<head>
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<meta charset="utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>The Spineless Tagless G-Machine — rlp documentation</title>
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<link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=4f649999" />
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<link rel="stylesheet" type="text/css" href="../_static/alabaster.css?v=039e1c02" />
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<script src="../_static/documentation_options.js?v=5929fcd5"></script>
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<script src="../_static/doctools.js?v=888ff710"></script>
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<script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
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<link rel="index" title="Index" href="../genindex.html" />
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<link rel="search" title="Search" href="../search.html" />
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<link rel="prev" title="Lexing, Parsing, and Layouts" href="layout-lexing.html" />
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<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
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<meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
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</head><body>
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<div class="document">
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<div class="documentwrapper">
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<div class="bodywrapper">
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<div class="body" role="main">
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<section id="the-spineless-tagless-g-machine">
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<h1>The <em>Spineless Tagless G-Machine</em><a class="headerlink" href="#the-spineless-tagless-g-machine" title="Link to this heading">¶</a></h1>
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<p>WIP. This will hopefully be expanded into a thorough walkthrough of the state
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machine.</p>
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<p>Evaluation is complete when a single <code class="code docutils literal notranslate"><span class="pre">NNum</span></code> remains on the stack and the
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dump is empty.</p>
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<div class="math">
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<p><img src="../_images/math/51b8ee3def56618c3d5c55841743d53ffbedbcfb.svg" alt="\transrule
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{ a : \nillist
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& \nillist
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& h
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\begin{bmatrix}
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a : \mathtt{NNum} \; n
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\end{bmatrix}
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& g
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}
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{ \mathtt{HALT}
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}"/></p>
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</div><p>Dereference an indirection passed as an argument to a function.</p>
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<div class="math">
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<p><img src="../_images/math/e91c8c9e0530c873480544a154b5156c1a3bc5cf.svg" alt="\transrule
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{a : s & d & h
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\begin{bmatrix}
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a : \mathtt{NAp} \; a_1 \; a_2 \\
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a_2 : \mathtt{NInd} \; a_3
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\end{bmatrix} & g}
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{a : s & d & h[a : \mathtt{NAp} \; a_1 \; a_3] & g}"/></p>
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</div><p>Dereference an indirection on top of the stack.</p>
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<div class="math">
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<p><img src="../_images/math/7a5577f4835bea58fb5e61feccfb2cac76ad365a.svg" alt="\transrule
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{p : s & d & h
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\begin{bmatrix}
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p : \mathtt{NInd} \; a
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\end{bmatrix} & g}
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{a : s & d & h & g}"/></p>
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</div><p>Perform a unary operation <img class="math" src="../_images/math/996b14e88c00afb0c157a014c7b04c192a6667d8.svg" alt="o(n)" style="vertical-align: -5px"/> with internal <code class="code docutils literal notranslate"><span class="pre">Prim</span></code> constructor
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<code class="code docutils literal notranslate"><span class="pre">O</span></code> on an argument in normal form.</p>
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<div class="math">
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<p><img src="../_images/math/758e69f9e44c00c28db11caa744ce8468e26062d.svg" alt="\transrule
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{ f : a : s
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{O} \\
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a : \mathtt{NAp} \; f \; x \\
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x : \mathtt{NNum} \; n
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\end{bmatrix}
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& g
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}
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{ a : s
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& d
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& h
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\begin{bmatrix}
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a : \mathtt{NNum} \; (o(n))
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\end{bmatrix}
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& g
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}"/></p>
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</div><p>Evaluate the argument of a unary operation with internal <code class="code docutils literal notranslate"><span class="pre">Prim</span></code>
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constructor <code class="code docutils literal notranslate"><span class="pre">O</span></code>.</p>
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<div class="math">
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<p><img src="../_images/math/9264520765ac3abdf00f5cff93232ef8f436c08c.svg" alt="\transrule
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{ f : a : \nillist
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{O} \\
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a : \mathtt{NAp} \; f \; x
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\end{bmatrix}
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& g
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}
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{ x : \nillist
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& (f : a : \nillist) : d
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& h
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& g
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}"/></p>
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</div><p>Restore the stack when a sub-computation has completed.</p>
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<div class="math">
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<p><img src="../_images/math/8dd8da75ac6612b08aa1c953fe79f69d9614a370.svg" alt="\transrule
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{ a : \nillist
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& s : d
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& h
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\begin{bmatrix}
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a : \mathtt{NNum} \; n
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\end{bmatrix}
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& g
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}
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{ s
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& d
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& h
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& g
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}"/></p>
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</div><p>Reduce a supercombinator and update the root with the <img class="math" src="../_images/math/cc9ad1bf37cbb0cbc3156f31e10ce7d8148d5e06.svg" alt="\beta" style="vertical-align: -4px"/>-reduced form</p>
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<div class="math">
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<p><img src="../_images/math/34e91bc0685dd54adb3e06c06e6fc0cc4d8ad419.svg" alt="\transrule
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{ a_0 : a_1 : \ldots : a_n : s
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& d
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& h
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\begin{bmatrix}
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a_0 : \mathtt{NSupercomb} \; [x_1,\ldots,x_n] \; e
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\end{bmatrix}
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& g
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}
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{ a_n : s
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& d
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& h'
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& g
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\\
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& \SetCell[c=3]{c}
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\text{where } h' = \mathtt{instantiateU} \; e \; a_n \; h \; g
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}"/></p>
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</div><p>Perform a binary operation <img class="math" src="../_images/math/a86f901ae855d64263ac2ab365517c5a7e5ccd14.svg" alt="o(x,y)" style="vertical-align: -5px"/> associated with internal <code class="code docutils literal notranslate"><span class="pre">Prim</span></code>
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constructor <code class="code docutils literal notranslate"><span class="pre">O</span></code> on two <code class="code docutils literal notranslate"><span class="pre">NNum</span></code> s both in normal form.</p>
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<div class="math">
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<p><img src="../_images/math/021357ee48ac0e35395fa99353083fee184026dd.svg" alt="\transrule
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{ f : a_1 : a_2 : s
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{O} \\
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a_1 : \mathtt{NAp} \; f \; (\mathtt{NNum} \; x) \\
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a_2 : \mathtt{NAp} \; a_1 \; (\mathtt{NNum} \; y)
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\end{bmatrix}
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& g
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}
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{ a_2 : s
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& d
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& h
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\begin{bmatrix}
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a_2 : \mathtt{NNum} \; (o(x,y))
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\end{bmatrix}
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& g
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}"/></p>
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</div><p>In a conditional primitive, perform the reduction if the condition has been
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evaluated as True (<code class="code docutils literal notranslate"><span class="pre">NData</span> <span class="pre">1</span> <span class="pre">[]</span></code>).</p>
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<div class="math">
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<p><img src="../_images/math/0a0458d62ece3f6e5019d53d0245ff5facdc5fdf.svg" alt="\transrule
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{ f : a_1 : a_2 : a_3 : s
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{IfP} \\
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c : \mathtt{NPrim} \; (\mathtt{NData} \; 1 \; \nillist) \\
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a_1 : \mathtt{NAp} \; f \; c \\
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a_2 : \mathtt{NAp} \; a_1 \; x \\
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a_3 : \mathtt{NAp} \; a_2 \; y
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\end{bmatrix}
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& g
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}
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{ x : s
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& d
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& h
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& g
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}"/></p>
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</div><p>In a conditional primitive, perform the reduction if the condition has been
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evaluated as False (<code class="code docutils literal notranslate"><span class="pre">NData</span> <span class="pre">0</span> <span class="pre">[]</span></code>).</p>
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<div class="math">
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<p><img src="../_images/math/5acebcc879cae1694dcc537b99796e0dc0e0ff05.svg" alt="\transrule
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{ f : a_1 : a_2 : a_3 : s
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{IfP} \\
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c : \mathtt{NPrim} \; (\mathtt{NData} \; 0 \; \nillist) \\
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a_1 : \mathtt{NAp} \; f \; c \\
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a_2 : \mathtt{NAp} \; a_1 \; x \\
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a_3 : \mathtt{NAp} \; a_2 \; y
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\end{bmatrix}
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& g
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}
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{ y : s
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& d
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& h
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& g
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}"/></p>
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</div><p>In a conditional primitive, evaluate the condition.</p>
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<div class="math">
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<p><img src="../_images/math/1d1d05c2792b02598e523fd646d6268749231320.svg" alt="\transrule
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{ f : a_1 : \nillist
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& d
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& h
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\begin{bmatrix}
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f : \mathtt{NPrim} \; \mathtt{IfP} \\
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a_1 : \mathtt{NAp} \; f \; x
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\end{bmatrix}
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& g
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}
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{ x : \nillist
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& (f : a_1 : \nillist) : d
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& h
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& g
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}"/></p>
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</div><p>Construct <code class="code docutils literal notranslate"><span class="pre">NData</span></code> out of a constructor and its arguments</p>
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<div class="math">
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<p><img src="../_images/math/a540630fbb5173bbf2de2d38326e10e6977b2c18.svg" alt="\transrule
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{ c : a_1 : \ldots : a_n : \nillist
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& d
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& h
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\begin{bmatrix}
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c : \mathtt{NPrim} \; (\mathtt{ConP} \; t \; n) \\
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a_1 : \mathtt{NAp} \; c \; x_1 \\
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\vdots \\
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a_n : \mathtt{NAp} \; a_{n-1} \; x_n
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\end{bmatrix}
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& g
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}
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{ a_n : \nillist
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& d
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& h
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\begin{bmatrix}
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a_n : \mathtt{NData} \; t \; [x_1, \ldots, x_n]
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\end{bmatrix}
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& g
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}"/></p>
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</div><section id="pairs">
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<h2>Pairs<a class="headerlink" href="#pairs" title="Link to this heading">¶</a></h2>
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<p>Evaluate the first argument if necessary</p>
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<div class="math">
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<p><img src="../_images/math/1fc5e2a4ce5b523a6e99c0937d45b0f285461097.svg" alt="\transrule
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{ c : a_1 : a_2 : \nillist
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& d
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& h
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\begin{bmatrix}
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c : \mathtt{NPrim} \; \mathtt{CasePairP} \\
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p : \mathtt{NAp} \; \_ \: \_ \\
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a_1 : \mathtt{NAp} \; c \; p \\
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a_2 : \mathtt{NAp} \; a_2 \; f
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\end{bmatrix}
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& g
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}
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{ p : \nillist
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& (a_1 : a_2 : \nillist) : d
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& h
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& g
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}"/></p>
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</div><p>Perform the reduction if the first argument is in normal form</p>
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<div class="math">
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<p><img src="../_images/math/d13e748def2419af7ed6d97286f8f8ba95d695ab.svg" alt="\transrule
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{ c : a_1 : a_2 : s
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& d
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& h
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\begin{bmatrix}
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c : \mathtt{NPrim} \; \mathtt{CasePairP} \\
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p : \mathtt{NData} \; 0 \; [x,y] \\
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a_1 : \mathtt{NAp} \; c \; p \\
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a_2 : \mathtt{NAp} \; a_1 \; f
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\end{bmatrix}
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& g
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}
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{ a_1 : a_2 : s
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& d
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& h
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\begin{bmatrix}
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a_1 : \mathtt{NAp} \; f \; x \\
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a_2 : \mathtt{NAp} \; a_1 \; y
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\end{bmatrix}
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& g
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}"/></p>
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</div></section>
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<section id="lists">
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<h2>Lists<a class="headerlink" href="#lists" title="Link to this heading">¶</a></h2>
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<p>Evaluate the scrutinee</p>
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<div class="math">
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<p><img src="../_images/math/f670f05da2f796ded634f483374c8523a2ed0ac4.svg" alt="\transrule
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{ c : a_1 : a_2 : a_3 : \nillist
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& d
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& h
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\begin{bmatrix}
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c : \mathtt{NPrim} \; \mathtt{CaseListP} \\
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a_1 : \mathtt{NAp} \; c \; x
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\end{bmatrix}
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& g
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}
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{ x : \nillist
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& (a_1 : a_2 : a_3) : \nillist
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& h
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& g
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}"/></p>
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</div><p>If the scrutinee is <code class="code docutils literal notranslate"><span class="pre">Nil</span></code>, perform the appropriate reduction.</p>
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<div class="math">
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<p><img src="../_images/math/2bfab760cd5a82cd980862645b628ea4c2a97f34.svg" alt="\transrule
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{ c : a_1 : a_2 : a_3 : s
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& d
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& h
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\begin{bmatrix}
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c : \mathtt{NPrim} \; \mathtt{CaseListP} \\
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p : \mathtt{NData} \; 1 \; \nillist \\
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a_1 : \mathtt{NAp} \; c \; p \\
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a_2 : \mathtt{NAp} \; p \; f_\text{nil} \\
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a_3 : \mathtt{NAp} \; a_2 \; f_\text{cons}
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\end{bmatrix}
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& g
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}
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{ a_3 : s
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& d
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& h
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\begin{bmatrix}
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a_3 : \mathtt{NAp} \; f_\text{nil}
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||||
\end{bmatrix}
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& g
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}"/></p>
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</div></section>
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||||
</section>
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||||
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||||
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||||
</div>
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||||
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||||
</div>
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||||
</div>
|
||||
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||
<div class="sphinxsidebarwrapper">
|
||||
<h1 class="logo"><a href="../index.html">rlp</a></h1>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
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||||
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||||
<h3>Navigation</h3>
|
||||
<p class="caption" role="heading"><span class="caption-text">Index</span></p>
|
||||
<ul>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../glossary.html">Glossary</a></li>
|
||||
</ul>
|
||||
<p class="caption" role="heading"><span class="caption-text">Commentary</span></p>
|
||||
<ul class="current">
|
||||
<li class="toctree-l1"><a class="reference internal" href="layout-lexing.html">Lexing, Parsing, and Layouts</a></li>
|
||||
<li class="toctree-l1 current"><a class="current reference internal" href="#">The <em>Spineless Tagless G-Machine</em></a></li>
|
||||
</ul>
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||||
|
||||
<div class="relations">
|
||||
<h3>Related Topics</h3>
|
||||
<ul>
|
||||
<li><a href="../index.html">Documentation overview</a><ul>
|
||||
<li>Previous: <a href="layout-lexing.html" title="previous chapter">Lexing, Parsing, and Layouts</a></li>
|
||||
</ul></li>
|
||||
</ul>
|
||||
</div>
|
||||
<div id="searchbox" style="display: none" role="search">
|
||||
<h3 id="searchlabel">Quick search</h3>
|
||||
<div class="searchformwrapper">
|
||||
<form class="search" action="../search.html" method="get">
|
||||
<input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
|
||||
<input type="submit" value="Go" />
|
||||
</form>
|
||||
</div>
|
||||
</div>
|
||||
<script>document.getElementById('searchbox').style.display = "block"</script>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
</div>
|
||||
</div>
|
||||
<div class="clearer"></div>
|
||||
</div>
|
||||
<div class="footer">
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||||
©2023, madeleine sydney ślaga.
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<a href="../_sources/commentary/stg.rst.txt"
|
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rel="nofollow">Page source</a>
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</div>
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|
||||
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</body>
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</html>
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